Book Summary: How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg

How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg

The Essence

Being wrong a lot less of the time means understanding that mathematics holds the secrets of navigating a world ruled by probabilities. Common sense tends to lie beyond the mathematical traps that day-to-day life lays. Such as falsely assuming linearity when the rate of change may not remain the same. Numbers may not always be what they seem to be, and it is our duty to apply the principles of mathematics to unveil the conventional approach to life as inherently flawed. How not to be wrong takes what math has learned about the world, and makes it palatable enough to avoid being mathematical bested by our lives (or at least understand when we are).

How Not to Be Wrong Journal Entry Notes:

This is my book summary of How Not to Be Wrong. My notes are a reflection of the journal write up above. Written informally, the notes contain a mesh and mix of quotes and my own thoughts on the book. Sometimes, to my own fault, quotes are interlaced with my own words. Though rest assured, I am not attempting to take any credit for the main ideas below. The Journal write up includes important messages and crucial passages from the book.

• Mathematics is the study of things that come out a certain way because there is no other way that they could possibly be.• The extension of common sense by other means.• Avoid thoughtless linear extrapolation: Not every curve is a line.• Twice a tiny number is a tiny number: Risk ratios applied to small numbers in probability can easily mislead us. • A mathematician is always asking: What assumptions are you making, are they justified?• Nonlinear thinking means which way you should go depends upon where you already are.• Diving one number by another is mere computation; figuring out what you should divide by what is mathematics.• When you’re testing a mathematical method, try computing the same thing several different answers, something is wrong with your method. • Math is like meditation, it puts you in direct contact with the universe, which is bigger than you, was here before you, and will be here after you.• A basic rule of mathematical life: If the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe does not object. • “P-Hacking”: Due to our publish or die culture, the science community runs a survivorship bias on themselves ‘To live or die by the .05’. We need statically insignificant data, the value is purely arbitrary and prompts dishonesty and elaborate verbal twists in our to be considered for publication. • The significant test is the detective, not the judge. • A significant test in an instrument, like a telescope. • What is improbable is probable.

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